e If Poisson is numberr of arrivals within a specified period of time, then the

Question

e If Poisson is numberr of arrivals within a specified period of time, then the uncertain time between arrivals has an exponential distribution. The E(T) = 1/m and the Var(T) = 1/m^2 e This is a discrete distribution QUESTION 6 10 points Arrivals come on average 2 per hour and follow an exponential distribution What is the "m" value per hour? questions to 3 decimals) What is the probability that an arrival will come in less than 15 minutes? (Answer to al What is the probability that an arrival will come in more than 15 minutes? What is the probability that no arrival will come in the next 15 minutes? QUESTION 7 10 points Which of the following is not true about the nomal distribution? Know as the Gaussian distribution

Explanation / Answer

Question 6

Here m value per hour = 2 per hour

1 arrival come in = 1/2 hour = 0.5 hour

(a) Pr(arrivals comes in less than 15 minutes) = EXP(t < 0.25; 0.5) = 1 - e-2t = 1 - e-2 * 0.25 = 0.3935

(b) Pr(t > 15 minutes) = e-2t = e-2 * 0.25 = 0.6065

(c) Expected number of arrivals in 15 minutes = 0.25 * 2 = 0.5

Pr( there will be no arrival in 15 minutes) = POISSON (X = 0 ; 0.5) = e-0.5 = 0.6065

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